General applicability and quantitative predictability of complex population-based crystallization models

结晶过程的建模有几个优点。精确和预测的数学模型已经并且可以用于理解潜在的物理，用于过程设计，优化和控制。在结晶领域，这些模型由固相的种群平衡方程（PBE）和液相的质量守恒约束组成。前者使人们能够模拟晶体集合的粒度和形状分布的演变。后者使人们能够模拟液相浓度/过饱和的演变。通常，这些模型是在学术环境中开发的，其规模和条件与现实的工业情景相去甚远。此外，尽管文献中发展的所有模型都考虑了“尺寸”的演变，但它们中的大多数都没有考虑晶体形状的演变（例如针状、板状等）。这些因素可能对结晶过程模型在不同规模（实验室到工业规模）的一般适用性和定量可预测性产生潜在影响。拜耳和曼彻斯特大学拟议的合作项目的总体目标是双重的。这些areG1。定量评价实验室规模模型预测能力的极限。提出一个可靠的实验验证框架，促进开发适用于不同尺度的预测结晶过程模型。这些目标将通过四个相互关联的计算和实验工作包（WPs）来实现。参考案例将是非专有的二元体系（一种溶质和一种溶剂），在实验室规模的纯生长条件下（500 mL至1 L），低悬浮密度（0.1-1 w/w%）。随后，将考虑其他现象（溶解，二次成核），复杂的溶剂系统，更高的悬浮密度（4-10 w/w%）和鳞片（100 mL至20 L）。预计该项目将帮助拜耳和更广泛的结晶界判断，在不同规模的可预测性以及投入的时间和资源方面，为工艺设计和操作开发工艺模型的重大努力是否值得。

Modeling of crystallization processes offer several advantages. Accurate and predictive mathematical models have been and can be used for understanding the underlying physics, for process design, optimization, and control. Within the domain of crystallization, these models are composed of population balance equations (PBE) for the solid phase and the mass conservation constraint for the liquid phase. The former enables one to model the evolution of the particle size and shape distribution of ensembles of crystals. The latter enables one to model the evolution of the liquid phase concentration/supersaturation. Often, these models are developed in an academic setting at scales and conditions that are far from a realistic industrial scenario. Additionally, even though all the models developed in the literature account for the evolution of "size", majority of them do not account for the evolution of the shape of crystals (e.g., needles, plates, etc.). These factors can have potential implications on the general applicability and quantitative predictability of crystallization process models across different scales (lab to industrial scale). The overarching goal of the proposed collaborative project between Bayer and University of Manchester is two-fold. These areG1. To quantitatively evaluate the limits of the predictive capability of lab-scale models.G2. To propose a sound experimentally validated framework that facilitates developing predictive crystallization process models applicable over different scales. These goals will be addressed using four interconnected computational and experimental work packages (WPs). The reference case will be a non-proprietary binary system (one solute and one solvent) under pure growth conditions in lab-scale (500 mL to 1 L) at low suspension densities (0.1-1 w/w%). Subsequently, additional phenomena (dissolution, secondary nucleation), complex solvent systems, higher suspension densities (4-10 w/w%), and scales (100 mL to 20 L) will be considered. It is anticipated that this project will help Bayer and the broader crystallization community to judge whether pursuing significant efforts in developing process models for process design and operation is worthwhile in terms of its predictability at different scales and the time and resources invested.